Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31774607 | C2 | semidirect |
| 3. #31774243 | C2 | semidirect |
| 4. #31774214 | C2 | semidirect |
| 5. #31774188 | C2 | semidirect |
| 6. #31774123 | C2 | semidirect |
| 7. #31774046 | C2 | semidirect |
| 8. C4×#16864641 | C2 | semidirect |
| 9. #31773962 | C2 | semidirect |
| 10. #102×D271 | C2 | semidirect |
| 11. #460×C271 | C2 | semidirect |
| 15. C2×C8×D271 | C22 | semidirect |
| 16. #22576160 | C22 | semidirect |
| 19. #22576136 | C22 | semidirect |
| 26. C4⋊C4×D271 | C22 | semidirect |
| 27. #22576092 | C22 | semidirect |
| 28. #22576091 | C22 | semidirect |
| 29. #22576084 | C22 | semidirect |
| 31. #22576081 | C22 | semidirect |
| 32. #22576081 | C22 | semidirect |
| 34. (C2×D271)⋊C8 | C22 | semidirect |
| 35. C4×C271⋊C8 | C22 | semidirect |
| 36. C2×SD16×C271 | C22 | semidirect |
| 38. C4×Q8×C271 | C22 | semidirect |
| 39. C4⋊C8×C271 | C22 | semidirect |
| 40. #102×C271 | C22 | semidirect |
| 84. D1084 | SD16 | semidirect |
| 136. C271 | #3295 | semidirect |
| 144. #460 | D271 | semidirect |
| 152. C2×SD16 | C2×D271 | semidirect |
| 162. C4×Q8 | C2×D271 | semidirect |
| 169. C4⋊C8 | C2×D271 | semidirect |
| 175. #102 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774607 | 2 |
| #31774532 | 2 |
| #31774243 | 2 |
| #31774214 | 2 |
| #31774188 | 2 |
| #31774123 | 2 |
| #31774046 | 2 |
| C4×#16864641 | 2 |
| #31773962 | 2 |
| #102×D271 | 2 |
| #460×C271 | 2 |
| #3295 | 271 |